1. Field of the Invention
The present invention generally relates to reflection seismology and, more particularly, to the migration of seismic data to provide images of subsurface formations that are located in geological media that cause seismic waves to be refracted so substantially that the waves turn upward.
2. State of the Art
One of the primary goals of reflection seismology is to obtain images of subsurface geological formations based upon information gleaned from surface recording of reflections of seismic waves that are purposefully directed into the earth. Toward that end, it is well known that seismic waves recorded at the earth's surface by geophones or hydrophones can be displayed in two- or three-dimensional seismic "time sections", each consisting of a large number of seismic traces.
Although visual inspection of seismic time sections can intuitively suggest the shape and location of subsurface reflecting formations, the visually-apparent images may be misleading as to the actual shape and location of the reflectors. For example, various geological conditions may cause signals reflected from a shallow formation to be received later than signals reflected from a deeper formation; where such conditions exist, visual consideration of time sections can lead to erroneous conclusions as to the positions of formations with respect to depth. Accordingly, it is ordinarily necessary to manipulate, or "migrate", recorded seismic data for the purpose of producing two- or three-dimensional images, called migrated sections, that depict the proper spatial locations of subsurface reflecting formations.
Migration processes for seismic data are usually computationally intensive One reason for the computational intensity is that seismic surveys, even small-scale ones, yield vast quantities of data. Thus, to avoid excessive data processing time and expense, migration algorithms should be efficient.
In practice, migration algorithms are based upon assumptions (i.e., models) concerning the geology that is being imaged. When actual geological conditions substantially deviate from expected subsurface conditions, a particular migration program may be ineffective or may produce misleading results. For example, a migration program that assumes a model of constant wave velocity throughout stratified formations may inaccurately depict the locations of subsurface formations where geological conditions cause wave velocities to increase rapidly with depth.
In the art of reflection seismology, seismic waves that substantially change direction with depth are called turning waves. Generally speaking, geological media that produce turning waves have the characteristic that the velocity of seismic waves increases with depth in the media. In some circumstances, directional changes are so substantial that wave fronts that were initially directed downward become horizontally directed, or even upwardly directed. During seismic surveys in such media, seismic waves may turn as they travel downward from a source, or as they travel upward from a reflector, or in both directions of travel.
Heretofore, there have not existed computationally efficient migration algorithms for imaging subsurface reflectors that reside in geological media that cause seismic waves to be refracted so substantially that the waves turn upward.